The linear and the third-order nonlinear optical properties of an exciton confined in a three-dimensional quantum dot with a parabolic potential are studied in a static magnetic field. Eigenvalues, wave functions, dipole matrix elements and selection rules are calculated analytically. Based on the calculated energies and wave functions, within the effective mass approximation, a compact-density matrix approach is employed to analyse the absorption coefficients and refractive index changes. The study is first of its kind since the excitonic effects are studied in a static magnetic field considering both the confinement potential and the electrostatic interaction between the electron-hole pair. An important finding of our research is the dependence of the magnitude of absorption coefficients on the radius of the quantum dot, the result that may have broad implications in future device designing.

在静磁场中研究了约束在具有抛物线势的三维量子点中的激子的线性和三阶非线性光学特性。分析计算特征值、波函数、偶极矩阵元素和选择规则。基于计算的能量和波函数，在有效质量近似内，采用紧凑密度矩阵方法来分析吸收系数和折射率变化。该研究是同类研究中的第一项，因为在静磁场中研究了激子效应，同时考虑了限制电位和电子-空穴对之间的静电相互作用。我们研究的一个重要发现是吸收系数的大小对量子点半径的依赖性，